Post Traumatic Stress Disorder is a psychiatric condition experienced by individuals after exposure to a traumatic event. Prior work has shown promise in detecting PTSD using physiological data such as heart rate. Despite the promise shown by the machine learning based algorithms for PTSD, the validation approaches used in previous research largely rely on theoretical and computational validation methods rather than naturalistic evaluations that account for users perceived precision and validity. Previous research has shown that users perceptions of physiological changes may not always align well with automated detection of such variables and such misalignment may lead to distrust in automated detection which may affect adoption or sustainable usage of such technologies. Therefore, the goal of this article is to investigate the perceived precision of the PTSD hyperarousal detection tool (developed previously) in a home study with a group of PTSD patients. Naturalistic evaluation of such data driven algorithms may provide foundational insight into the efficacy of such tools for non intrusive and cost efficient remote monitoring of PTSD symptoms and will pave the way for their future adoption and sustainable use. The results showed over sixty five percent of perceived precision in naturalistic validation of the detection tool. Further, the results indicated that longitudinal exposure to the detection tool might calibrate users trust in automation.